Pakistan army soldiers stand guard near the compound where it is believed Osama bin Laden lived in Abbottabad. Photograph: Anjum Naveed/AP

President Asif Ali Zardari has hit back against American accusations that his country secretly sheltered Osama bin Laden, who was killed on Sunday night, and has claimed Pakistan played a role in leading US special forces to the al-Qaida leader.

"Some in the US press have suggested that Pakistan lacked vitality in its pursuit of terrorism, or worse yet that we were disingenuous and actually protected the terrorists we claimed to be pursuing," Zardari said.

"Such baseless speculation may make exciting cable news, but it doesn't reflect fact."

It was the first high-level rebuttal by the Pakistani government after a day of trenchant criticism from US commentators and officials, who questioned how the Saudi fugitive managed to live for years in a town housing one of Pakistan's most prestigious military facilities.

The dramatic 40-minute air assault that killed Bin Laden was carried out by US Navy Seals who crossed from Afghanistan in four helicopters and targeted a house in Abbottabad, a two-hour drive north of Islamabad. The spacious $1m (£600,000) compound is located a few streets from the Pakistan Military Academy, the country's equivalent of Sandhurst or West Point.

"People have been referring to this as hiding in plain sight. We are looking at how he was able to hide out there for so long," said the White House counter-terrorism adviser, John Brennan.

It was "inconceivable" that Bin Laden did not enjoy a "support system" in Pakistan, he said.

Writing in the Washington Post, Zardari said his country was "the world's greatest victim of terrorism", called Bin Laden "the source of the greatest evil of the new millennium", and claimed that Pakistan had played a role in identifying the al-Qaida courier who ultimately led US forces to Bin Laden.

"Although the events of Sunday were not a joint operation, a decade of co-operation and partnership between the United States and Pakistan led up to the elimination of Osama bin Laden as a continuing threat to the civilised world," he said.

The US secretary of state, Hillary Clinton, perhaps anxious not to alienate a partner still vital to actions against al-Qaida, appeared to partly agree. "In fact, co-operation with Pakistan helped lead us to Bin Laden and the compound in which he was hiding," she said.

Zardari's comments will please Pakistan's powerful military, the real target of US accusations of double dealing. The army's spokesman has been silent over the Abbottabad operation, although senior officials from Pakistan's ISI intelligence agency insisted they had not been informed beforehand.

The army faces many questions as well as anger over the breach of sovereignty, including how a fleet of US helicopters managed to fly through Pakistan's air defences and return to Afghanistan unhindered.

Precise details about Bin Laden's final moments are still emerging. US officials said he was killed by gunfire in the final stages of the 40-minute assault, as was one of his sons and his youngest wife. The White House claimed she had been used by Bin Laden as a human shield.

Bin Laden, codenamed Geronimo for the operation, was shot twice, in the head and chest. Brennan denied the soldiers were under orders to kill, not capture. "If we had the opportunity to take him alive, we would have done," he said.

After his death soldiers shouted "Geronimo EKIA", meaning enemy killed in action. His body was taken by helicopter to a US aircraft carrier in the Arabian Gulf and buried at sea.

Barack Obama said: "The world is safer. It is a better place because of the death of Osama bin Laden."

Such was the American distrust of the notoriously leaky Islamabad government that it did not even inform it of the raid in its own territory until after the helicopters had cleared Pakistani airspace.

Members of Congress have threatened to withhold economic aid to Pakistan over the affair.

Carl Levin, a Democrat who heads the powerful Senate armed services committee, reflected scepticism in the US about Bin Laden's ability to remain hidden in Pakistan.

"I think the Pakistani army and intelligence have a lot of questions to answer given the location, the length of time and the apparent fact that this facility was actually built for Bin Laden and its closeness to the central location of the Pakistani army," he told a press conference.

The US is expected to step up pressure on Pakistan to hand over the Taliban leader, Mullah Omar and Bin Laden's deputy, Ayman al-Zawahiri, if they are in Pakistan. The death of Bin Laden could also lead to a rethink of the scale of US involvement in Afghanistan.

Embassies, airports and defence bases were placed on high alert for possible retaliation by al-Qaida sympathisers. The Pakistani Taliban threatened attacks against the country's government and military, and the US. In a phone call to Reuters, a spokesman said: "Now Pakistani rulers, President Zardari and the army will be our first targets. America will be our second target".

The US embassy and its three consulates in Pakistan were closed to the public until further notice. David Cameron warned of a continuing threat from "extremist terrorism" but hailed a "massive step forward".

The mood in the US was one of celebration as Americans gathered at Ground Zero in New York, pleased finally to have retribution. Obama will visit the site of the World Trade Centre on Thursday to meet the families of those killed in the September 11 attacks.

Clinton suggested that US policy on Afghanistan would not shift, but other officials hinted the dynamics may have changed. The Pentagon only wants to see a token force of a few thousand withdrawn beginning in the summer, but Obama may want a more significant reduction.

An Afghan government official said he feared Bin Laden's death would give "justification for US premature disengagement from the region". It was a view echoed by Ahmed Wali Massoud, an Afghan politician and brother of Ahmed Shah Massoud, the legendary resistance fighter who was assassinated just two days before the September 11 attacks on the orders of Bin Laden.

"Already the US has been thinking about shifting its policy on the war on terror and there is a risk that the American public will continue to question why their troops are still fighting there," he said.

One of the most senior US officers serving in Afghanistan, General William Caldwell, told the Guardian the death might encourage moderate elements within the Taliban to give up.

John Taylor, whose daughter Carrie, 24, was killed in the 7/7 bombings in London in 2005, said he would be celebrating. "This is poetic justice for my daughter. This is a little piece of justice for Carrie and the thousands around the world who have been killed as a result of [Bin Laden's] actions."